TY - JOUR
T1 - Sorting permutations
T2 - Games, genomes, and cycles
AU - Adamyk, K. L.M.
AU - Holmes, E.
AU - Mayfield, G. R.
AU - Moritz, D. J.
AU - Scheepers, M.
AU - Tenner, B. E.
AU - Wauck, H. C.
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, (cds) and context directed reversal, (cdr). These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates. This paper investigates mathematical aspects of these two sorting operations. The main result of this paper is a generalization of previously discovered characterizations of cds-sortability of a permutation. The combinatorial structure underlying this generalization suggests natural combinatorial two-player games. These games are the main mathematical innovation of this paper.
AB - Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, (cds) and context directed reversal, (cdr). These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates. This paper investigates mathematical aspects of these two sorting operations. The main result of this paper is a generalization of previously discovered characterizations of cds-sortability of a permutation. The combinatorial structure underlying this generalization suggests natural combinatorial two-player games. These games are the main mathematical innovation of this paper.
KW - Permutation sorting
KW - context directed block interchanges
KW - context directed reversals
KW - fixed point sorting game
KW - misere game
KW - normal play game
UR - http://www.scopus.com/inward/record.url?scp=85034015032&partnerID=8YFLogxK
U2 - 10.1142/S179383091750063X
DO - 10.1142/S179383091750063X
M3 - Article
AN - SCOPUS:85034015032
SN - 1793-8309
VL - 9
JO - Discrete Mathematics, Algorithms and Applications
JF - Discrete Mathematics, Algorithms and Applications
IS - 5
M1 - 1750063
ER -